In this paper, we provide relations among the following properties:(a) the tail triviality of a probability measure μ on the configuration space ϒ; (b) the finiteness of a suitable L2-transportation-type distance d¯ϒ; (c) the irreducibility of local μ-symmetric Dirichlet forms on ϒ. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including sine2, Airy2, Besselα,2 (α ≥ 1), and Ginibre point processes. In particular, the case of the unlabelled Dyson Brownianmotion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role
